Problem $5(4$ points$)$: Consider a simple planetary gear set. The sun gear has $60$ teeth, and the planet has $22$ teeth. Inputs to the system are the carrier or arm, and the sun gear. The carrier arm rotates at $100$ rpm counterclockwise, and the sun gear rotates at $150$ rpm clockwise. The ring gear is drawn in dark blue. The planet is the idler gear. Denoting clockwise rotation as positive,

Using the tabular method and showing all steps involved, obtain a relationship between the angular velocity of the output and the inputs.

Using the information given, determine the overall gear train reduction ratio, and the speed of rotation of the ring and the planet gear if the sun and carrier rotate at the rates and directions shown.

If the sun gear were fixed, and the ring was the input, and the carrier the output, determine the reduction ratio.